Meshgrid fo variables in complex equation

I have an equation that have three variables

The equation is like this : f(x, y, z)=2x+3y+4z=0

But the equation I really want to use is more complex that I can’t turn it into

z=(-3y-2x)/4 format like this

And I want to draw a plot about the relation between the three(x, y, z) when

x = 3: 1:6; (3,4,5,6)

y = 5: 1:9; (5,6,7,8,9)

I know that if I can turn the equation into z=(-3y-2x)/4 format, I can do that using

x=3:1:6;
y=5:1:9;
[xx,yy]=meshgrid(x,y);
zz=(-3.*yy-2.*xx)/4;
mesh(xx,yy,zz);

But because the equation I really want to use is too complex, I can’t use the method to get the answer I want

I also try the other way using for loop

i=1
for x= 3:1:6
    for y= 5:1:9
        syms f(z)
        f=2*x+3*y+4*z;
        answer=solve(f);
        answer2(i)=answer;
        x1(i)=x;
        y1(i)=y;
        i=i+1;
       
    end
end
answer3=double(answer2);
[x2,y2]=meshgrid(x1,y1);

But still don’t know the next process

Can I have other methods to use, or can I revise the methods above to solve my problem?

I am new to matlab, and i really need your help, thank you!

Answer 1

[Stephan]

You might want to try fimplicit3:

syms f(x,y,z)
f(x, y, z)=2*x+3*y+4*z==0

f(x, y, z) = 

fimplicit3(f)

or an even more complex example:

f(x, y, z)=2*sin(x)+tanh(3*y)+exp(z/4)==0

f(x, y, z) = 

fimplicit3(f)

[HSIUYUAN WANG]

Thank you very much for your answer, that's very helpful to me. But I also have another question, when I want to add an interval

syms f(x,y,z)
f(x,y,z)=2.*x+3.*y+4.*z==0
interval=[3 6 5 9 0 5];
fimplicit3(f,interval)

it will get

But when I use

syms f(x,y,z)
f(x,y,z)=2.*x+3.*y+4.*z==0
interval=[-3 6 -5 9 0 5];
fimplicit3(f,interval)

It can get

Is that because the interval I set must be negative to positive when I use the fimplicit3?

Thanks again for your useful suggestion and reply!

[Stephan]

See the documentation, the syntax is:

fimplicit3(f,[xmin xmax ymin ymax zmin zmax])

read example here:

https://de.mathworks.com/help/symbolic/fimplicit3.html#bvcxpkx-19

[HSIUYUAN WANG]

I'll try that later, thank you very much!